[Highland Park] Fence laws

My husband and I own a home in Highland Park and would like to build a wooden fence on the back side of our property. There is already a chain link fence where we want to build ours. I am wondering if anyone knows if there is a zoning process we need to go through to do this, or if it is different depending on if we replace the existing fence or build a new one next to the old one. Any thoughts or recommendations welcome. Thanks, Cara